I think fiat over lightning is a really bad idea. I'm surprised more people aren't talking about it. It has so many perverse incentives, its not even funny. I could see it as a convenience layer for a merchant perhaps, but I don't think this fantasy of a bunch of HODLers running a network of exchange nodes is going to go anywhere.
Here's a potential application for it: a:
  • Customer pays merchant in bitcoin with lightning
  • Merchant converts bitcoin to dollars for his own internal accounting
b:
  • Customer pays merchant in dollars with lightning
  • Merchant keeps payment in dollars
When merchant ends up with too much bitcoin and needs more dollars:
  • Merchant opens bitcoin channel with liquidity exchange
  • Liquidity exchange opens dollar channel with Merchant
  • Merchant exchanges bitcoin for dollars with lightning with circular route
Here's the problem with this all; How do the fiat channels settle when they are closed if they aren't using a stablecoin? Anytime you open a fiat channel, you'll need to have a written contract with your channel partner to settle manually through your bank.
How do the fiat channels settle when they are closed if they aren't using a stablecoin?
I don't remember anybody planning to have fiat channels without stablecoins. All the projects like Taro and RGB include on-chain stablecoins exactly because of the problem you mentioned.
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